Typical trace-distance relaxation concentrates around a mean in open quantum systems, producing typical mixing times separated from worst-case by rare-state bottlenecks that scale logarithmically, linearly, or exponentially depending on the slow modes.
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In 1D overdamped relaxation, hard or soft walls—not well count or metastability—determine whether the Mpemba effect appears.
For 1D polynomial double-well potentials, the classical Mpemba effect is not caused by the double-well shape but by a hard wall on the shallow side (or a steeper tail), vanishing in an infinite system.
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Typical Mixing and Rare-State Bottlenecks in Open Quantum Systems
Typical trace-distance relaxation concentrates around a mean in open quantum systems, producing typical mixing times separated from worst-case by rare-state bottlenecks that scale logarithmically, linearly, or exponentially depending on the slow modes.
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Predicting the conditions for observing the Mpemba effect
In 1D overdamped relaxation, hard or soft walls—not well count or metastability—determine whether the Mpemba effect appears.
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The Mpemba effect likes to hit a wall
For 1D polynomial double-well potentials, the classical Mpemba effect is not caused by the double-well shape but by a hard wall on the shallow side (or a steeper tail), vanishing in an infinite system.